We study the generation of non-Gaussianity in models of hybrid inflation withtwo inflaton fields, (2-brid inflation). We analyse the region in the parameterand the initial condition space where a large non-Gaussianity may be generatedduring slow-roll inflation which is generally characterised by a large f_NL,tau_NL and a small g_NL. For certain parameter values we can satisfytau_NL>>f_NL^2. The bispectrum is of the local type but may have a significantscale dependence. We show that the loop corrections to the power spectrum andbispectrum are suppressed during inflation, if one assume that the fieldsfollow a classical background trajectory. We also include the effect of thewaterfall field, which can lead to a significant change in the observablesafter the waterfall field is destabilised, depending on the couplings betweenthe waterfall and inflaton fields.